Without randomized controlled trials, there's no easy way to separate the effects of increased educational spending and tutoring from hundreds of other factors that might affect someone's admission rate. Clearly we expect it helps or we wouldn't spend money on it. But it's not clear if educational spending is the dominant factor in academic success or a small factor among many.
In at least one study I've seen, smaller class size didn't have much effect, but private tutoring did.
As someone who has privately tutored many rich kids vs poor kids for nearly a decade, I don't think I need to see a study to see how much more advantages they have. It's pretty apparent the advantages.
Yes a really "dumb" kid will still be "dumb" academically, but people here are severely underestimating what money can buy in education. I've seen really "dumb" kids be brought up to the level of "passably smart" simply because of resource access.
When you have teachers who are not overworked and are paid lovely salaries (ie 6 figure salaries), imagine every teacher you have actually cares and invested in your education? Imagine every class has recordings of every lecture as well as a curriculum that has a lot of forethought and time put into it? And imagine if the school has a lacking teacher, than the parents hire some ex-olympian, or ex-superstar coach or teacher to make up for that? I've seen parents hire ex-olympic athletes to get some untalented rich kid to close to olympic level.
Honestly, I think it's really understated how much educational spending can affect a kid. Most people will not see what I've seen, and even from someone who came from a middle class background who used to believe wealth does not matter when it came to education, even I was shocked by what money can buy in "academic success" and my opinion changed. I at this point, don't need to see a study because it was that drastic.
Anecdotally, I heard a story from a teacher I worked with who spent a lot of time with a student who was lagging behind their peers in school and was given extra support through the special education program. Their family decided to move away, so the school put together a file about how the student's progress. They later heard that the receiving school system found that student to be far ahead of their peers and put them into a gifted program.
There is such a difference in environments in this country's education system. I was doing math in my sophomore year of high school that some don't see until college (or ever). Was I inherently smarter? Of course not. I had good teachers and books, I didn't have to work a job at night, etc.
In at least one study I've seen, smaller class size didn't have much effect, but private tutoring did.